Answer:
3 2/3 will be 3 10/15
1 4/5 will be 1 12/15
Divide 3 into 15 and get 5; 5 x 2 = 10
Divide 5 into 15 and get 3; 3 x 4 = 12
So new equivalent fractions are 3 10/15
and 1 12/15
Step-by-step explanation:
The required equivalent fractions for 3 10/15 and 1 12/15.
Given, two mixed fractions 3 2/3 and 1 4/5, determine equivalent fractions using 15 as the common denominator.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
First
= 3 2/3
= 3 + 2 / 3
= 3 + 2 × 5 / 3 × 5
= 3 + 10 / 15
Second,
= 1 4 / 5
= 1 4 × 3 / 5 × 3
= 1 12/15
Thus, the required equivalent fractions for 3 10/15 and 1 12/15.
Learn more about simplification here: https://brainly.com/question/12501526
#SPJ3
Which statement describes the inverse of m(x) = x^2 – 17x?
a. The domain restriction x ≥ StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction minus StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
b. The domain restriction x ≥ StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction + StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
c. The domain restriction x ≥ Negative StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction minus StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
d.The domain restriction x ≥ Negative StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction + StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
Given:
The function is
[tex]m(x)=x^2-17x[/tex]
To find:
The inverse of the given function.
Solution:
We have,
[tex]m(x)=x^2-17x[/tex]
Substitute m(x)=y.
[tex]y=x^2-17x[/tex]
Interchange x and y.
[tex]x=y^2-17y[/tex]
Add square of half of coefficient of y , i.e., [tex]\left(\dfrac{-17}{2}\right)^2[/tex] on both sides,
[tex]x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2[/tex]
[tex]x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2[/tex]
[tex]x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
Taking square root on both sides.
[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}[/tex]
Add [tex]\dfrac{17}{2}[/tex] on both sides.
[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y[/tex]
Substitute [tex]y=m^{-1}(x)[/tex].
[tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex]
We know that, negative term inside the root is not real number. So,
[tex]x+\left(\dfrac{17}{2}\right)^2\geq 0[/tex]
[tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex]
Therefore, the restricted domain is [tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex] and the inverse function is [tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex].
Hence, option D is correct.
Note: In all the options square of [tex]\dfrac{17}{2}[/tex] is missing in restricted domain.
Answer:
C on edu
Step-by-step explanation:
How do you solve this? Without going into anything to complicated as this should be Year 10 maths
Given : ABCD is a square with each side 5cm .
To Find : The area of the shaded region .
Solution : On observing the figure we can see two quadrants , quadrant ADC & quadrant ABC .
If we join A to C , then it will be common for triangles ADC & ABC . And they will be congruent by SSS congruence condition.
Therefore the area of both quadrants will also be equal . Now we can find area of quadrant as ;
[tex]\large\boxed{\red{\bf Area_{quadrant}=\dfrac{\pi r^2}{4}}}[/tex]
Here radius will be equal to 5cm .
⇒ Area = πr² / 4 .
⇒ Area = π (5cm)² / 4 .
⇒ Area = 22/7 × 25 × 4 cm².
⇒ Area = 19.64 cm² .
So , total area of both quadrants = 39.28 cm² .
Also , area of square will be :
[tex]\large\boxed{\bf{\red{Area_{square}=(side)^2}}}[/tex]
⇒ Area = 5cm × 5cm .
⇒ Area = 25 cm².
Now , subtract area of one quadrant from the area of square = 25cm² - 19.64 cm² = 5.36 cm².
Similarly area of other white region = 5.36cm² .
And the areas sum will be = 5.36cm² × 2 = 10.72cm² .
Now , from the figure it's clear that ,
⇒ Area of unshaded region + Area of shaded region = 25cm².
⇒ 10.72cm² + ar( Shaded region ) = 25cm².
⇒ ar ( Shaded region ) = 25cm² - 10.72cm².
⇒ ar ( Shaded region ) = 14.28 cm².
Hence the area of shaded region is 14.28 cm².
[tex]\large\boxed{\red{\bf Answer = 14.28cm^2}}[/tex]
Juan’s cell phone company charges $35 a month for phone service with limited data for every gigabyte of data overage the company charges $15 write an equation that represents how many gigabytes one goes over in a month if his bill was $110
Answer:15x+35=110
Step-by-step explanation:
A mug is 3/7 full. The mug contains 1/2 cup of water. Find the capacity of the mug
Answer:
7/6 cups of water is the mug's capacity
Step-by-step explanation:
Capacity refers to how much a container can contain.
Let x be the capacity of the mug.
According to the question, the mug is 3/7 full. This means that the mug contains 3/7 × x = 3x/7 of water.
It was further stated that the mug contains 1/2cup of water. This means that:
1/2 cup of water = 3x/7 of water in the mug
Hence;
1/2 = 3x/7
3x × 2 = 7 × 1
6x = 7
x = 7/6
Therefore, the capacity of that mug is 7/6 cups of water.
The capacity of the the mug if it is 3/7 full and contains 1/2 cup of water is 7/6 cup
CapacityGiven:
Quantity of the mug = 1/2 cuplet
x = full capacity of the mugWater in the mug = 3/7 of x
= 3/7x
Note:
Water in the mug = 1/2 cup
So,
3/7x = 1/2
divide both sides by 3/7x = 1/2 ÷ 3/7
= 1/2 × 7/3
= 7/6
Therefore, the full capacity of the mug is 7/6 cup
Learn more about fraction:
https://brainly.com/question/2929160
What’s the value of y in this picture
Answer: A 83
Step-by-step explanation:
Add 46 to 51 then subtract from 180 to get the correct answer(83)
ASAP!!! PLEASE HELP
10 points
CHECK PHOTO Intercepts of the graph BE SURE TO BE CORRECT PLEASE no work needed
Answer:
y= (0, .7)
x= (-1.2, 0)
Step-by-step explanation:
r u taking a test?
help with this immediately
Answer:
c
Step-by-step explanation:
%gggggyyhhttbu6gnmk8tg
Determine whether each equation is true or false.
-5/-1 = 5
(0/-4) = 0
-3/1 = -3
- 8/0 = 0
Step-by-step explanation:
1.False
2.True
3.True
4.False
8. Fay Teng's expenditures for the past 3 months were: August,
$1,735.50; September, $1,829.42; and October, $1,793.88.
What is her average monthly expenditure?
9. You use the utility company's budget plan for paying your
home heating bills. You pay $75 a month for 9 months. Your
actual bills are: September, $28.95; October, $16.15; November,
$68.46; December, $109.34; January, $115.26; February. $94.19;
March $75.66; April, $51.97; and May, $49.16. Compute the
average for the 9 months.
ght The McGraw-e Companies, Inc. All rights
=$75.66 all in all and $67.99 dollars
Somebody please answer this question I’m begging you
Answer: The answer is A, the y value increases by 1.5 as the x value increases by 1. Therefore A does not describe the graph.
How is 5 represented in 6.75
Answer:
5 is in the hundreths place :))
Step-by-step explanation:
Answer:
0.05
Step-by-step explanation:
since the place value of the five is beyond the decimal point, and it is the second number beyond the decimal point, so it is in the hundredths place.
The following are a list of variables that will almost certainly vary across students in a large undergraduate introductory statistics course.
(a) Favorite beverage
(b) Year of birth
(c) Typing speed
(d) Handedness (e.g., left or right handed)
(e) Age
(f) Occupation
(g) Self-report of Assertiveness
For questions 1a to 1d that follow choose the variable or variables that best represent the level of measurement.
a) Which variables would typically be measured on a nominal scale of measurement?
b) Which variable would likely be measured on an interval, but not a ratio scale?c) Which two variables are most likely to be measured on a ratio scale?d) As typically measured, which variable represents at least an ordinal scale of measurement, but probably not a true interval scale?
Step-by-step explanation:
a. nominal scales
occupation
Favorite beverage
b. Interval but not ratio.
Typing speed
c. ratio scale.
age
Handedness (e.g., left or right handed)
d. Ordinal scale of measurement but not a true interval scale.
Self-report of Assertiveness
year of birth
Kenya went to the convenience store to buy some candy bars for her friends. She spent a total of $6.00 on candy bars. Each candy bar cost $1.50.
How many candy bars did Kenya buy?
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Find the equation of the line passing through the points (-2,-4) and (7,23)
Answer:
y=−5.4x
Step-by-step explanation:
Slope -5.4
Intercept -14.80
Eight more than.twice an number is four less than the same number
Answer:
2x+8=x-4
Step-by-step explanation:
I think that's right, let me know if it's wrong and I'll delete
This table gives a few (x, y) pairs of a line in the coordinate plane. What is the x-intercept of the line?
Answer:
(22,0)
Step-by-step explanation:
22 0
35 -15
48 -30
61 -45
74 -60
Help me please!!..,,
Answer:
A.
Step-by-step explanation:
1.5 x 0.1 = 0.15
0.15 inches
Dont know if this is for sure right. Hope it is.
Pls Help :( 15 points
108 students went on a field trip. Three buses were filled and 27 students traveled in cars. How many students were in each bus?
Please include algebraic equation please.
Answer:
(108-27)/3 =27
Each bus has 27 students, because 108-27=81, 81/3=27
Step-by-step explanation:
Hope this helps! <3
5 1/5- 1 3/4 fractions
Answer:
3 9/20
Step-by-step explanation:
first find a common demonator and change the denomators and what ever you did to the bottom you do to the top, then subtract them.
Which shows another way to write 9.54?
O 0.5 + 0.04
O 9+ 0.4 + 0.05
O (9 * 1) + (5 x 0.1) + (4 x 0.01)
O (9 x 0.1) + (5 x 0.01) + (4 x 0.001)
Answer:
It would be C
Step-by-step explanation:
If necessary, combine like terms. (5x+1)(5x-1)
Answer:2 5x^2-1
Step-by-step explanation:
someone help please!!
Answer:
1
Step-by-step explanation:
Ik y’all good at math, help me out yall!
Answer:
i think the answer be 150 feet per minute
hope this is right
Answer:
150
Step-by-step explanation:
use points on the line i'll use (2,300) and (1,150)
m=y2-y1/x2-x1
300-150=150
2-1=1
150/1=150
hope this helps :3
sorry if im wrong
PLEASE HELP PLEASE!!
Complete the following statement to estimate the root of 75 to the nearest tenth. Use numbers that are closest to the root of 75
Y-4>3 solve the question
Answer:
y>7
Step-by-step explanation:
y-4>3
+4 +4
y>7
To solve the problem -9 + 18 what is the first step?
a. KCO (keep change fli[p)
b. Subtract 18 - 9
c. Subtract 9 - 18
d. Add 9 + 18
Answer:
Step-by-step explanation:
Help the pic is right here
Answer:
i think its C
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
its just division tbh
The regular price of a bathing suit is $89.99. Estimate the sale price of the 25 points
bathing suit at 70% off regular price.
$27.00
$82.99
$19.99
A popular restaurant advertises that it delivers its orders within 30 minutes. Suppose the average delivery time for one store is 27 minutes with a standard deviation of three minutes. One particular order delivery has a z-score of –2.15. Which of the following statements is not a correct interpretation?
A.The delivery time was 2.15 standard deviations below the average delivery time.
B.The delivery time was less than the average delivery time by 2.15 standard deviations.
C.The delivery time was faster than the average delivery time by 2.15 standard deviations.
D.The delivery time was slower than the average delivery time by 2.15 standard deviations.
Answer: B. The delivery time was less than the average delivery time by 2.15 standard deviations.
Step-by-step explanation:
Given: A popular restaurant advertises that it delivers its orders within 30 minutes.
Suppose the average delivery time for one store is 27 minutes with a standard deviation of 3 minutes.
z-score value represents the number of standard deviations is the data value is far from mean.
Here, z-score = -2.15 which clearly indicates that the delivery time was 2.15 standard deviations below( '-' sign suggest value is below mean) the average delivery time.
Hence, the correct option is B.
Answer:
B
Step-by-step explanation: